Analytic fermionic Green’s functions from holography

To refer to this page use:
http://arks.princeton.edu/ark:/88435/pr13067

Abstract:

We find exact, analytic solutions of the Dirac equation for a charged, massless fermion in the
background of a charged, dilatonic black hole in
AdS
5
. The black hole descends from type IIB
supergravity, where it describes D3-branes with equal angular momenta in two of the three independent
planes of rotation orthogonal to the world-volume. The Green’s function near the Fermi surface for a
strongly coupled fermionic system can be extracted holographically from an exact solution of the Dirac
equation at zero frequency but nonzero momentum. There can be several Fermi momenta, and they take
the form
k
F
¼
q
n
1
=
2
(in units of the chemical potential), where
q
is the charge of the spinor, and
n
is a non-negative integer that labels the Fermi surfaces. Much as for holographic Fermi surfaces based on
the Reissner-Nordstro
̈
m-
AdS
5
solution, the dispersion relation of the excitations near the Fermi surface is
determined by the geometry close to the horizon, and one can obtain Fermi liquid, marginal Fermi liquid,
and non-Fermi liquid behaviors depending on the value of
k
F
.